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Polynomials with Special Regard to Reducibilityby A. Schinzel; G.-C. Rota
Cambridge University Press 2000; US$ 139.00This unique book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Also included are results based on recent work of E. Bombieri and U. Zannier. more...
Complex Polynomialsby T. Sheil-Small; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak
Cambridge University Press 2002; US$ 70.00This book studies the geometric theory of polynomials and rational functions in the plane. The theory is carefully constructed bearing in mind the needs of graduate students. Several unsolved problems are presented as well as the full solutions to some well known conjectures. more...
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Scienceby Andrew J. Sommese; Charles W. Wampler
World Scientific 2005; US$ 78.00Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980?s to the most recent research on positive dimensional sets. more...
Walsh Equiconvergence of Complex Interpolating Polynomialsby Amnon Jakimovski
Springer 2006; US$ 129.00A collection of the various old and new results, centered around the following simple observation of J L Walsh. This book is particularly useful for researchers in approximation and interpolation theory. more...
Numerical Methods for Roots of Polynomials by J.M. McNamee
Elsevier 2007; US$ 175.00This book (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton?s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent?s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled ?A Handbook of Methods for Polynomial Root-finding?. This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. - First comprehensive treatment of Root-Finding in several decades. - Gives... more...
Polynomials and Vanishing Cyclesby Mihai Tibar
Cambridge University Press 2007; US$ 100.00A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations; contains the latest research findings. more...
Positive Trigonometric Polynomials and Signal Processing Applicationsby Bogdan Dumitrescu
Springer 2007; US$ 139.00Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications. more...
The Center and Cyclicity Problemsby Valery G. Romanovski; Douglas S. Shafer
Springer 2009; US$ 59.95Using a computational algebra approach, this text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. It covers the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. more...
Lectures on N_X(p)by Jean-Pierre Serre
CRC Press 2011; US$ 39.95Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in a context that is appealing to specialists in number theory and algebraic geometry. Along with covering open problems, the text examines the size and congruence properties of NX(p) and describes the ways in which it is computed, by closed formulae and/or using efficient computers. The first four chapters cover the preliminaries and contain almost no proofs. After an overview of the main theorems... more...
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